A new multilinear insight on Littlewood's 4/3-inequality

摘要

We unify Littlewood's classical 4/3-inequality (a forerunner of Grothendieck's inequality) together with its rn-linear extension due to Bohnenblust and Hille (which originally settled Bohr's absolute convergence problem for Dirichlet series) with a scale of inequalties of Bennett and Carl in e_p-spaces (which are of fun_damental importance in the theory of eigenvalue distribution of power compact operators). As an application we give estimates for the monomial coefficients of homogeneous e_p-valued polynomials on c_0.